Generalizations of the Moran effect explaining spatial synchrony in population fluctuations

The Moran effect for populations separated in space states that the autocorrelations in the population fluctuations equal the autocorrelation in environmental noise, assuming the same linear density regulation in all populations. Here we generalize the Moran effect to include also nonlinear density regulation with spatial heterogeneity in local population dynamics as well as in the effects of environmental covariates by deriving a simple expression for the correlation between the sizes of two populations, using diffusion approximation to the theta-logistic model. In general, spatial variation in parameters describing the dynamics reduces population synchrony. We also show that the contribution of a covariate to spatial synchrony depends strongly on spatial heterogeneity in the covariate or in its effect on local dynamics. These analyses show exactly how spatial environmental covariation can synchronize fluctuations of spatially segregated populations with no interchange of individuals even if the dynamics are nonlinear.     

有色环境噪音对空间异质种群动态同步性的影响

随着种群动态和空间结构研究兴趣的增加,激发了大量的有关空间同步性的理论和实验的研究工作。空间种群的同步波动现象在自然界广泛存在,它的影响和原因引起了很多生态学家的兴趣。Moran定理是一个非常重要的解释。但以往的研究大多假设环境变化为空间相关的白噪音。越来越多的研究表明很多环境变化的时间序列具有正的时间自相关性,也就是说用红噪音来描述更加合理。因此,推广经典的Moran效应来处理空间相关红噪音的情形很有必要。利用线性的二阶自回归过程的种群模型,推导了两种群空间同步性与种群动态异质性和环境变化的时间相关性(即环境噪音的颜色)之间的关系。深入分析了种群异质性和噪音颜色对空间同步性的影响。结果表明种群动态异质性不利于空间同步性,但详细的关系比较复杂。而红色噪音的同步能力体现在两方面:一方面,本身的相关性对同步性有贡献;另一方面,环境变化时间相关性可以通过改变种群密度依赖来影响同步性,但对同步性的影响并无一致性的结论,依赖于种群的平均动态等因素。这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义。     

Environmental colour intensifies the Moran effect when population dynamics are spatially heterogeneous

Evidence for synchronous fluctuations of spatially separated populations is ubiquitous in the literature, including accounts within and across taxa. Among the few mechanisms explaining this phenomenon is the Moran effect, whereby independent populations are synchronized by spatially correlated environmental disturbances. The body of research on the Moran effect predominantly assumes that environmental disturbances within a local site are serially uncorrelated; that is, successive observations in time at a particular local site are independent. Yet, many environmental variables are known to possess strong temporal autocorrelation – a character which has often been described as 'colour'. The omission of environmental colour from research on the Moran effect may be due in part to the lack of methods capable of generating sets of time series with a desired colour and spatial correlation. Here I present a novel and simple method designated as 'phase partnering' to generate such sets of time series and I investigate the combined impact of spatial correlation and environmental colour on population synchrony in two common models of population dynamics. For linear population dynamics, and for a subset of nonlinear population dynamics, coloured environments intensify the Moran effect when population dynamics are spatially heterogeneous; in coloured environments the spatial correlation between populations more closely mimics the spatial correlation between their respective environments. Given that most environmental variables are coloured, these results imply that the Moran effect may be a far more significant driver of regional-scale population and interspecific synchrony than is currently believed.     

Population synchrony and environmental variation: an experimental demonstration

Understanding the causes of population synchrony is an important issue for population management. Its study in field populations involves disentangling the effects of dispersal and correlated environmental noise. Here we report on an experimental investigation of the synchronizing effects of noise in closed laboratory populations of a soil mite, Sancassania berlesei . Mite life-histories are highly plastic with respect to resource availability (which is a function of food supply and population density). By varying the food supply we imposed environmental variation. We show that (a) population synchrony is a function of environmental synchrony, (b) perceived population synchrony depends on the life-history stage counted, and (c) average population synchrony tends to be lower than environmental synchrony: even when populations were supplied with food with a correlation of 1.0, the correlation between populations was 0.63 (bootstrapped 95%CI 0.54–0.71). This supports recent theoretical work suggesting that the Moran theorem (indicating that population synchrony equals environmental synchrony) generally overestimates the population synchrony of nonlinear systems.     

Spatially autocorrelated disturbances and patterns in population synchrony

Spatially synchronous population dynamics have been documented in many taxa. The prevailing view is that the most plausible candidates to explain this pattern are extrinsic disturbances (the Moran effect) and dispersal. In most cases disentangling these factors is difficult. Theoretical studies have shown that dispersal between subpopulations is more likely to produce a negative relationship between population synchrony and distance between the patches than perturbations. As analyses of empirical data frequently show this negative relationship between the level of synchrony and distance between populations, this has emphasized the importance of dispersal as a synchronizing agent. However, several weather patterns show spatial autocorrelation, which could potentially produce patterns in population synchrony similar to those caused by dispersal. By using spatially extended versions of several population dynamic models, we show that this is indeed the case. Our results show that, especially when both factors (spatially autocorrelated perturbations and distance-dependent dispersal) act together, there may exist groups of local populations in synchrony together but fluctuating asynchronously with some other groups of local populations. We also show, by analysing 56 long-term population data sets, that patterns of population synchrony similar to those found in our simulations are found in natural populations as well. This finding highlights the subtlety in the interactions of dispersal and noise in organizing spatial patterns in population fluctuations.     

Red environmental noise and the appearance of delayed density dependence in age-structured populations

Previous work suggests that red environmental noise can lead to the spurious appearance of delayed density dependence (DDD) in unstructured populations regulated only by direct density dependence. We analysed the effect of noise reddening on the pattern of spurious DDD in several variants of the density-dependent age-structured population model. We found patterns of spurious DDD in structured populations with either density-dependent fertility or density-dependent survival of the first age class, inconsistent with predictions from unstructured population models. Moreover, we found that nonspurious negative DDD always emerges in populations with deterministic chaotic dynamics, regardless of population structure or the type of environmental noise. The effect of noise reddening in generating spurious DDD is often negligible in the chaotic region of population deterministic dynamics. Our findings suggest that differences in species' life histories may exhibit different patterns of spurious DDD (owing to noise reddening) than predicted by unstructured models.     

Spatial synchrony in population fluctuations: extending the Moran theorem to cope with spatially heterogeneous dynamics

The recent interest in the spatial structure and dynamics of populations motivated numerous theoretical and empirical studies of spatial synchrony, the tendency of populations to fluctuate in unison over regional areas. The first comprehensive framework applied to spatial synchrony was probably the one elaborated by P. A. P. Moran back in 1953. He suggested that if two populations have the same linear density-dependent structure, the correlation between them will be equal to that between the local density-independent conditions. Surprisingly, the consequences of violating the assumption that the dynamics of the populations are identical has received little attention. In this paper, making the assumption that population dynamics can be described by linear and stationary autoregressive processes, I show that the observed spatial synchrony between two populations can be decomposed into two multiplicative components: the demographic component depending on the values of the autoregressive coefficients, and the correlation of the environmental noise. The Moran theorem corresponds to the special case where the demographic component equals unity. Using published data, I show that the spatial variability in population dynamics may substantially contribute to the spatial variability of population synchrony, and thus should not be neglected in future studies.     

Does the pattern of population synchrony through space reveal if the Moran effect is acting?

The populations of many species fluctuate in synchrony across large geographical areas. This synchrony is often attributed to the Moran effect, that is, shared environmental fluctuations across the region. In this article, I use a series of simple metapopulation models to show that the degree of synchrony among populations separated by different distances is strongly affected by the particular way that environmental stochasticity is represented in the models. Furthermore, when multiple types of stochasticity are acting simultaneously, the synchronizing effect of any one type is difficult to discern from the resulting pattern of population synchrony. These effects can be exacerbated under certain demographic conditions or if population dynamics are affected by interspecific interactions. In general, it should be extremely difficult to determine if synchrony is caused by the Moran effect using only the synchrony–distance relationship of natural populations.     

The Moran effect revisited: spatial population synchrony under global warming

The world is spatially autocorrelated. Both abiotic and biotic properties are more similar among neighboring than distant locations, and their temporal co-fluctuations also decrease with distance. P. A. P. Moran realized the ecological importance of such ‘spatial synchrony’ when he predicted that isolated populations subject to identical log-linear density-dependent processes should have the same correlation in fluctuations of abundance as the correlation in environmental noise. The contribution from correlated weather to synchrony of populations has later been coined the ‘Moran effect’. Here, we investigate the potential role of the Moran effect in large-scale ecological outcomes of global warming. Although difficult to disentangle from dispersal and species interaction effects, there is compelling evidence from across taxa and ecosystems that spatial environmental synchrony causes population synchrony. Given this, and the accelerating number of studies reporting climate change effects on local population dynamics, surprisingly little attention has been paid to the implications of global warming for spatial population synchrony. However, a handful of studies of insects, birds, plants, mammals and marine plankton indicate decadal-scale changes in population synchrony due to trends in environmental synchrony. We combine a literature review with modeling to outline potential pathways for how global warming, through changes in the mean, variability and spatial autocorrelation of weather, can impact population synchrony over time. This is particularly likely under a ‘generalized Moran effect’, i.e. when relaxing Moran's strict assumption of identical log-linear density-dependence, which is highly unrealistic in the wild. Furthermore, climate change can influence spatial population synchrony indirectly, through its effects on dispersal and species interactions. Because changes in population synchrony may cascade through food-webs, we argue that the (generalized) Moran effect is key to understanding and predicting impacts of global warming on large-scale ecological dynamics, with implications for extinctions, conservation and management.     

Analysing the Moran effect and dispersal: their significance and interaction in synchronous population dynamics

Population synchrony over various geographical scales is known from a large number of taxa. Three main hypotheses have been put forward as explanations to this phenomenon. First, correlated environmental disturbances (so called Moran effect). Moran showed that at least for linear models, the population synchrony would exactly match that of the corresponding environment. Second, the migration, or dispersal, of individuals is liable to cause population synchrony. Third, nomadic predators have been proposed as a synchronising mechanism. In this paper, I analyse the first two explanations by linearizing a general population model with spatial structure. From this linear approximation I derive an expression for the population synchrony. The major results are: 1) Population synchrony can vary significantly depending on the timing of the population census. 2) The environmental correlation is always important. It sets the 'base level' of synchrony. 3) Dispersal is only an effective synchronising mechanism when the local dynamics are at least close to unstable. 4) These results are valid even in a model with delayed density dependence – with possibly cyclic dynamics. Time lag structure has little effect on synchrony. Some of the predictions presented here are supported by data from the literature.     

The extended Moran effect and large-scale synchronous fluctuations in the size of great tit and blue tit populations

1. Synchronous fluctuations of geographically separated populations are in general explained by the Moran effect, i.e. a common influence on the local population dynamics of environmental variables that are correlated in space. Empirical support for such a Moran effect has been difficult to provide, mainly due to problems separating out effects of local population dynamics, demographic stochasticity and dispersal that also influence the spatial scaling of population processes. Here we generalize the Moran effect by decomposing the spatial autocorrelation function for fluctuations in the size of great tit Parus major and blue tit Cyanistes caeruleus populations into components due to spatial correlations in the environmental noise, local differences in the strength of density regulation and the effects of demographic stochasticity. 2. Differences between localities in the strength of density dependence and nonlinearity in the density regulation had a small effect on population synchrony, whereas demographic stochasticity reduced the effects of the spatial correlation in environmental noise on the spatial correlations in population size by 21.7% and 23.3% in the great tit and blue tit, respectively. 3. Different environmental variables, such as beech mast and climate, induce a common environmental forcing on the dynamics of central European great and blue tit populations. This generates synchronous fluctuations in the size of populations located several hundred kilometres apart. 4. Although these environmental variables were autocorrelated over large areas, their contribution to the spatial synchrony in the population fluctuations differed, dependent on the spatial scaling of their effects on the local population dynamics. We also demonstrate that this effect can lead to the paradoxical result that a common environmental variable can induce spatial desynchronization of the population fluctuations. 5. This demonstrates that a proper understanding of the ecological consequences of environmental changes, especially those that occur simultaneously over large areas, will require information about the spatial scaling of their effects on local population dynamics.     

Climate mediated exogenous forcing and synchrony in populations of the oak aphid in the UK

Contemporary population dynamics theory suggests that animal fluctuations in nature are the result of the combined forces of intrinsic and exogenous factors. Weather is the iconic example of an exogenous force. The common approach for analyzing the relationship between population size and climatic variables is by simple correlation or using the climate as an additive covariable in statistical models. Here, we evaluated different functional forms in which climatic variables could influence population dynamics of the oak aphid Tuberculatus annulatus both in each locality and in relation to synchrony between localities. Results indicate that in at least four of eight aphid populations, climate influences population dynamics by modifying the carrying capacity of the system (lateral effect mediated by winter precipitation). Additionally, path analysis showed that synchrony in population dynamics is highly correlated with synchrony in winter precipitation regime, and the spatial scale of both processes is similar, which suggests that this is an example of the Moran effect. Our results show the key effects of precipitation on intra and inter population processes of this aphid. The methods used, mixing population dynamics modelling and test of synchrony, allowed us to connect the direct and indirect effects of exogenous variables into each population with patterns of synchrony inter populations.     

Biological filtering of correlated environments: towards a generalised Moran theorem

Many species from diverse taxa are known to display synchronous fluctuations across vast geographical ranges. It is often thought that climate factors influencing the growth of conspecific populations are correlated over large distances and hence produce the synchronous population dynamics – an effect known as the Moran effect. However, for species embedded in a food web the Moran effect needs not necessarily influence the focal species directly, but can act indirectly through other species. Such an indirect synchronization can also occur in an age-structured population, where the correlated environment of one age-class causes synchronous fluctuations of another. Here, we investigate this indirect Moran effect. We find first of all that synchrony is readily transferred through food webs or between age classes, which complicates the identification of the underlying synchronizing factor. Secondly, we find puzzling cases, where synchrony is enhanced as it is filtered through a food web or between age-classes. Our results also apply to systems of different species, but with closely matching dynamics.     

INTRODUCTION

Foliage-feeding forest insects have served as model systems in the study of animal populations for more than 50 years. Early studies emphasized identification of "key" mortality agents or density-dependent sources of mortality. However, these efforts became burdened by rhetorical ambiguity, and population ecologists are increasingly focusing on characterizing population behavior and identifying the processes that generate that behavior. Two types of behavior seem to be common in forest insect populations: periodic oscillations ("population cycles") and spatial synchrony (synchronous fluctuations over large geographic areas). Several population processes (e.g., host–pathogen interactions) have been demonstrated to be capable of producing periodic oscillations, but the precise identity of these processes remains uncertain for most forest insects and presents a challenge to future research. As part of these efforts, a greater emphasis is needed on the use of statistical methods for detecting periodic behavior and for identifying other types of population behavior (e.g., equilibrium dynamics, limit cycles, transient dynamics). Spatial synchrony appears to be even more ubiquitous in forest insect populations. Dispersal and regional stochasticity ("Moran effect") have been shown to be capable of producing synchrony, but again more research is needed to determine the relative contribution of these processes to synchrony observed in natural populations. In addition, there is a need to search for other types of time–space patterns (e.g., traveling waves, spiral waves) in forest insect populations and to determine their causes. Received: April 25, 2000 / Accepted: September 22, 2000     

When can dispersal synchronize populations?

While spatial synchrony of oscillating populations has been observed in many ecological systems, the causes of this phenomenon are still not well understood. The most common explanations have been the Moran effect (synchronous external stochastic influences) and the effect of dispersal among populations. Since ecological systems are typically subject to large spatially varying perturbations which destroy synchrony, a plausible mechanism explaining synchrony must produce rapid convergence to synchrony. We analyze the dynamics through time of the synchronizing effects of dispersal and, consequently, determine whether dispersal can be the mechanism which produces synchrony. Specifically, using methods new to ecology, we analyze a two patch predator-prey model, with identical weak dispersal between the patches. We find that a difference in time scales (i.e. one population has dynamics occurring much faster than the other) between the predator and prey species is the most important requirement for fast convergence to synchrony.     

Synchrony of spatial populations induced by colored environmental noise and dispersal

Spatial synchrony of oscillating populations has been observed in many ecological systems, and its influences and causes have attracted the interest of ecologists. Spatially correlated environmental noises, dispersal, and trophic interactions have been considered as the causes of spatial synchrony. In this study, we develop a spatially structured population model, which is described by coupled-map lattices and incorporates both dispersal and colored environmental noise. A method for generating time series with desired spatial correlation and color is introduced. Then, we use these generated time series to analyze the influence of noise color on synchrony in population dynamics. The noise color refers to the temporal correlation in the time series data of the noise, and is expressed as the degree of (first-order) autocorrelation for autoregressive noise. Patterns of spatial synchrony are considered for stable, periodic and chaotic population dynamics. Numerical simulations verify that environmental noise color has a major influence on the level of synchrony, which depends strongly on how noise is introduced into the model. Furthermore, the influence of noise color also depends on patterns of dispersal between local populations. In addition, the desynchronizing effect of reddened noise is always weaker than that of white noise. From our results, we notice that the role of reddened environmental noise on spatial synchrony should be treated carefully and cautiously, especially for the spatially structured populations linked by dispersal.     

Life history strategies affect climate based spatial synchrony in population dynamics of West African freshwater fishes

Spatial synchrony in species abundance is a general phenomenon that has been found in populations representing virtually all major taxa. Dispersal among populations and synchronous stochastic effects (the so called "Moran effect") are the mechanisms most likely to explain such synchrony patterns. Very few studies have related the degree of spatial synchrony to the biological characteristics of species. Here we present a case where specific predictions can be made to relate river fish species characteristics and synchrony determined exclusively by a Moran effect through the expected sensitivity of species to the regional component of environmental stochasticity. By analyzing 23-year time series of abundance estimates in two isolated localities we show that species associated with synchronized reproduction during the wet season, high fecundity, small egg size and high gonado-somatic index (the so called "periodic" strategy) have a higher degree of spatial synchrony in population dynamics than species associated with the opposite traits (the so called "equilibrium" strategy). This is supported by significant relationships (P values <0.01) between species traits and the levels of synchrony after removing taxonomical relatedness. Spatial synchrony computed from summed annual total catches by groups of species, separated into strategy types also showed a significantly higher degree of synchrony for the periodic (r=0.83) than the equilibrium (r=0.46) group. Regional hydrological variability is likely to be partly responsible for the observed synchrony pattern and a regional discharge index showed better relationships with the periodic group, supporting the expected differential effect of regional environmental correlation on population dynamics.     

Northern Atlantic Oscillation effects on the temporal and spatial dynamics of green spruce aphid populations in the UK

1. The role of climate variability in determining the spatial and temporal patterns of numerical fluctuations is a central problem in ecology. The influence of the North Atlantic Oscillation (NAO) index on the population dynamics and spatial synchrony of the green spruce aphid Elatobium abietinum across the UK was shown. 2. Fifteen overlapping time series within the UK were analysed; we used nonparametric models for determining the feedback nonlinear structure and the climatic effects. The spatial synchrony of these populations and the relationship between synchrony and NAO was estimated. 3. From the 15 time series across the UK, 11 showed positive and significant NAO effects. In most of the cases the NAO effects were nonlinear showing strong negative effects of low values. The NAO variation improve the explained variance of the first-order feedback models in 14.5%; ranging from 0% to 48%. All data showed strong-nonlinear (concave) feedback structure. In most of the localities the explained variance by the first-order feedback was about 50-60%. 4. The spatial synchrony of the per capita growth rates and residuals is high across long distances for those populations affected by NAO. The correlation function predicts a spatial scale of synchrony of about 350-400 km for NAO influenced populations. 5. We think that simple population theoretical models describing the link between NAO fluctuations and green spruce aphid dynamics may be fundamental for predicting and simulating the consequences of different climatic scenarios of the future.     

Spatial synchrony of recruitment in mountain-dwelling woodland caribou

Spatial synchrony in population dynamics is a ubiquitous feature across a range of taxa. Understanding factors influencing this synchrony may shed light on important drivers of population dynamics. Three mechanisms influence the degree of spatial synchrony between populations: dispersal, shared predators, and spatial environmental covariance (the Moran effect). We assessed demographic spatial synchrony in recruitment (calf:cow ratio) of 10 northern mountain caribou herds in the Yukon Territory, Canada (1982–2008). Shared predators and dispersal were ruled out as causal mechanisms of spatial recruitment synchrony in these herds and therefore any spatial synchrony should be due to the Moran effect. We also assessed the degree of spatial synchrony in April snow depth to represent environmental variability. The regional average spatial synchrony in detrended residuals of April snow depth was 0.46 (95% CI 0.37 to 0.55). Spatial synchrony in caribou recruitment was weak at 0.13 (95% CI −0.06 to 0.32). The spatial scale of synchrony in April snow depth and caribou recruitment was 330.2 km (95% CI 236.3 to 370.0 km) and 170.0 km (95% CI 69.5 to 282.8 km), respectively. We also investigated how the similarity in terrain features between herds influenced the degree of spatial synchrony using exponential decay models. Only the difference in elevation variability between herds during calving was supported by the data. Herds with more similar elevation variability may track snowmelt ablation patterns in a more similar fashion, which would subsequently result in more synchronized predation rates on calves and/or nutritional effects impacting juvenile survival. Interspecific interactions with predators and alternate prey may also influence spatial synchrony of recruitment in these herds.